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2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify...
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices ...
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2)
3. Let (a) Show that F is conservative...
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2...
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'...
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curv...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and l...
Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and let r( + F.dr Evaluate
Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and let r( + F.dr Evaluate
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r,...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Def...
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Define dsup(f,g)-sup |f(t)-g(t) and di(f.g)f (t)- g(t)ldt (f,g E C) tEI (i) Prove that dsup is a metric on C (ii) Prove that di is a metric on C. (You may use any standard properties of continuous functions and integrals, provided you make your reasoning clear.) 6 i) Let 1 denote the constant function on I with value 1. Give an explicit...
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the...
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the line integral S ry ryds. 1/V2. 1/2, V2, 0,
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y...
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y + z = 4, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate $.F. F.dr. F= (32² + 3y² + sin x? )i + (6xy + 3z)j + (x2 + 2yz)k $. F. dr= (Type an exact answer.) с
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2)
3. Let (a) Show that F is conservative...
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
QB(27pts)(a). Evaluate the circulation ofF(xy)-<x,y+x> on the curve r(t)=<2cost, 2sinp, foross2n (b) Evaluate J F.dr, where C is a piecewise smooth path from (1,0) to (2,1) and F- (e'cos x)i +(e'sinx)j [Hint: Test F for conservative (c). Use green theorem to express the line integral as a double integral and then evaluate. where C is the circle x+y-4 with counterclockwise orientation. (d(Bonus10 pts) Consider the vector field Foxyz) a. Find curl F y, ,z> F.dr where C is the curve...
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
3. Evaluate |F.dr w tine integral is independent of path. Compute F-dr and C is the ellipse given with the counter clockwise rotation Answer by 7-6--4 4 Evaluate vf-dr where (x.y)-d C is the curve shown below. Answer. |vf.dr=-4
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and let r( + F.dr Evaluate
Let 8yx9 F(x, y, z)(9x8 In(4y2 + 10) + 6z7)i 3г) ј + (42x26 + Зу - 7sin zez) k ( + + 4y210 k,0 sts 1 (3+1)i (22)j and let r( + F.dr Evaluate
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
B2. (a) Let I denote the interval 0,1 and let C denote the space of continuous functions I-R. Define dsup(f,g)-sup |f(t)-g(t) and di(f.g)f (t)- g(t)ldt (f,g E C) tEI (i) Prove that dsup is a metric on C (ii) Prove that di is a metric on C. (You may use any standard properties of continuous functions and integrals, provided you make your reasoning clear.) 6 i) Let 1 denote the constant function on I with value 1. Give an explicit...
3. Let C be the curve r(t) = < sint, cost, t>,0 sts 1/2. Evaluate the line integral S ry ryds. 1/V2. 1/2, V2, 0,
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y + z = 4, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate $.F. F.dr. F= (32² + 3y² + sin x? )i + (6xy + 3z)j + (x2 + 2yz)k $. F. dr= (Type an exact answer.) с
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